hiemstar / iga-demos

isogeometric analysis demo

iga-demos

This repository contains an isogeometric analysis demos for 2D linear elasticity.

In this demo we discretize the classical linear elatostatics equations using the Galerkin method based on isogeometric function spaces. We follow the notation used in [1] and Bezier extraction [2]. A more mathematical view on the finite element method can be found in [3]. Regarding isogeometric analysis we refer to the first paper [4] and the book [5].

[1] Hughes, Thomas JR. The finite element method: linear static and dynamic finite element analysis. Courier Corporation, 2012.

[2] Borden, Michael J., et al. "Isogeometric finite element data structures based on Bézier extraction of NURBS." International Journal for Numerical Methods in Engineering 87.1‐5 (2011): 15-47.

[3] Strang, Gilbert, and George J. Fix. An analysis of the finite element method. Vol. 212. Englewood Cliffs, NJ: Prentice-Hall, 1973.

[4] Hughes, T.J., Cottrell, J.A. and Bazilevs, Y., 2005. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39), pp.4135-4195.

[5] Cottrell, J. Austin, Thomas JR Hughes, and Yuri Bazilevs. Isogeometric analysis: toward integration of CAD and FEA. John Wiley & Sons, 2009.